1
                                                                    Exhibit 23.1

                        CONSENT OF DELOITTE & TOUCHE LLP

    We consent to the incorporation by reference in this Amendment No. 2 to the
Current Report on Form 8-K under the Securities Exchange Act of 1934 of LSI
Logic Corporation dated June 15, 2001, as amended, of our report dated January
18, 2001 (March 26, 2001 as to Note 18) and contained in Registration Statement
No. 333-58862 of LSI Logic Corporation on Form S-4 under the Securities Act of
1933 insofar as such report relates to the financial statements of C-Cube
Microsystems Inc. for the year ended December 31, 2000.

/s/ DELOITTE & TOUCHE LLP

San Jose, California

July 16, 2001